Santa Syllogisms

It is important for everyone, though especially programmers and lawyers, to be able to think clearly. You need to be able to conclude only true things from the facts you know. A syllogism, from the Greek words for conclusion and inference, is a logic puzzle where you draw a conclusion from particular kinds of claimed facts you are given and from those facts alone.

As long as the facts are true the conclusion follows (though if the ‘facts’ are not actually true then nothing really is known).

If the following supposed facts were true what could you conclude?

1.
All presents in the sack are for good children.All teddies in the sack are presents (in the sack).Therefore we can conclude which of the following?a. only some teddies in the sack are for good children.b. all teddies in the sack are for good children.c. only some presents in the sack are for good children.
d. none of the above.

2.
No elves are unhappy.All who work for Santa are elves.
Therefore we can conclude which of the following?a. All who work for Santa are unhappy.b. All elves work for Santa.c. Some who work for Santa are unhappy.d. No one who works for Santa is unhappy.

3.Anything that has good brakes is fast.
Santa’s sleigh is fast.Therefore we can conclude which of the following?a. Santa's sleigh has good brakes.b. Santa needs a break.c. All sleighs have good brakes.d. None of the above.

4.
All lazy creatures are bad at helping Santa.
Some elves are lazy creatures.Therefore we can conclude which of the following:a. All elves are bad at helping Santa.b. Some elves are bad at helping Santa.c. No lazy creatures are elves.d. None of the above.

5.
All elves are helpful.Some magical creatures are not helpful.Therefore we can conclude which of the following:a. Some magical creatures are not elves.b. All magical creatures are helpful.c. All elves are not magical creatures.d. None of the above.

More to come …

Answers

With the following answers we give general reasoning patterns that generate other valid conclusions from facts. Just substitute your own words in for X, Y and Z and you will get your own valid statements. The conclusions will only be true if the facts are of course, but the statement as a whole will be true whether the conclusion is or not.

1. We can conclude:

b. All teddies in the sack are for good children

We can use the reasoning pattern

All X are YAll Y are Z.MEANS WE CAN CONCLUDEAll X are Z
where
X is "teddies in the sack"
Y is "presents in the sack"
Z is "for good children"

2. We can conclude:

d. No one who works for Santa is unhappy.

We can use the reasoning pattern

No X are YAllZ are XMEANSNo Z are Y
where
X is "elves"
Y is "unhappy"
Z is "who work for Santa"

3. We can conclude:

d. None of the above.

We can’t use any reasoning patterns as the two facts do not chain together. They are just separate facts about different things that are fast.

4. We can conclude:

b. Some elves are bad at helping Santa.

We can use the reasoning pattern

All X are YSome Z are XMEANSSome Z are Y
where
X is "lazy creatures"
Y is "bad at helping Santa"
Z is "elves"

5. We can conclude:

a. Some magical creatures are not elves.

We can use the reasoning pattern

All X are YSome Z are not YMEANSSome Z are not X
where
X is "elves"
Y is "helpful"
Z is "magical creatures"